The multiplicative (×) identity is written as 1 and the multiplicative inverse of a is written as a−1. Most theories that are now recognized as parts of algebra started as collections of disparate facts from various branches of mathematics, acquired a common theme that served as a core around which various results were grouped, and finally became unified on a basis of a common set of concepts. This book is intended for a one-year introductory course in abstract algebra with some topics of an advanced level.

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